FTL, from what I have heard.

As a preface to my question, I am in no way asserting a FTL posibility which violates the posulates of Special Relativity. Throughout several online articles and books that I have been reading, there has been a referance to some sort of warping of spacetime that allows you to, in their words, "beat a light beam". This involves the warping of spacetime, expressed in an analogy of "cutting a sheet of paper into a cone".

However I still do not 'fully' understand this concept, it is to my knowledge that, according to the book (which was written by a prinston professor), "you can travel through the light cone, beat a beam of light, and come back to earth and shake hands with yourself." That's not an exact quote, and I can give you more exact references to what was said in the book if you would like.

Originally, I thought that you beat the light beam and hence you were able to merly see yourself take off. But by him asserting that you can shake hands with yourself as you begin to take off, he must be stating that yourself in the past is a physiclly existing entity, and not just light beams that you are seeing.

So which one is it : merly seeing the light photons carrying the information of "you taking off", or physiclly co-existing with your past-self and hence being able to "shake your hand before take off"?

When people talk about "beating a light beam," they (rather surprisingly) are not talking about going faster than the speed of light.

Imagine if you had a region of space severely warped by the presence of some very small, very massive object. The usual example is a "cosmic string," which is a essentially a hypothetical object that is essentially a very thin "line" of very dense matter.

If you shine a light beam across the gravitational well created by this very thin string, the light will potentially take a very long time to get across the well. (Remember that time appears to run more slowly deep in a gravitational well, so you, on the outside, would consider the light to be moving through the well very slowly).

You, at the outskirts of the gravitational well, are less effected. In some situations, you could actually go around the circumference of the well in less time (according to your watch) that the light took going straight across it.

In analogy, consider two ants trying to get from one side of the rim of a bowl to the other. One ant goes down through the bowl's center and up the other side, while the other ant just walks around the rim. For bowls of a certain shape, the circumferential journey will take less time than the straight-across journey.

This doesn't break general relativity, because general relativity doesn't say you can't beat a light beam through a severely curved region of space by judicious choice of path. General relativity only says that you cannot beat the speed of light locally.

If you fire a beam of light in one direction, and then walk another direction, general relativity certainly permits the possibility of getting to some given destination point in less time than the light.

None of this can be used for time travel to the past, though.

Imagine that you fire up a video projector and send its light through a severely curved region of space so that it eventually arrives at a screen a long way away. Imagine that you let the projector run for a half hour, then take the "shortcut," arriving at the screen via a different, faster route than the light went. When you get to the screen, you might see the movie playing from, say, the opening scene -- even though you already let the projector run for 30 minutes. That's the sort of "time travel" you can achieve with this method. You're definitely not really travelling backwards in time -- you're just outrunning the light.

This doesn't break general relativity, because general relativity doesn't say you can't beat a light beam through a severely curved region of space by judicious choice of path. General relativity only says that you cannot beat the speed of light locally.

If you fire a beam of light in one direction, and then walk another direction, general relativity certainly permits the possibility of getting to some given destination point in less time than the light.

Well Warren I am not so sure about that, would you care to give some support for those assertions?

Basically you are saying that in GR it is possible that there exists a space-time topology where a sub lightspeed non geodesic path from A to B can outrun a light beam going from A to B.

Except for the case of a light beam getting stuck inside a black hole I do not see that that is obvious at all.

Take a simple case like of a light beam coming from a far away nebula passing our sun and going toward us. Yes it is true that from our perspective the beam slows down due to the sun's gravity, but is there a faster path? Something could go around the influence of the sun's gravity but that means a longer path so more time, furthermore such a path is at sub lightspeed, so how does it add up to be the faster path?
Yes you could argue that the curvature in this example is weak, but the stronger the curvature the longer the path we have to take to avoid its influence.

Well, MeJennifer, you better brush up on your relativity, because the only "speed of light" that is well defined is the local speed of light, and it's the local speed of light that you cannot surpass.

Basically you are saying that in GR it is possible that there exists a space-time topology where a sub lightspeed non geodesic path from A to B can outrun a light beam going from A to B.

That's not what I said.

Relativity certainly does not preclude there being two or more geodesics, in the same region of spacetime, connecting the same two events, yet one longer than the other. This freedom is also the basis of wormholes, which are certainly permissible in the theory.

If you care to demonstrate mathematically how such situations are not admissible, I'd love to see you try.

It was written by a university professor, yet not a well-known one. The more general concept of time travel with cosmic string is known as the "Gott Loop," and you can find tons of references on the web.

Relativity certainly does not preclude there being two or more geodesics, in the same region of spacetime, connecting the same two events, yet one longer than the other. This freedom is also the basis of wormholes, which are certainly permissible in the theory.

Correct, but you claim that the one going around the gravitational field can get there sooner, which by the way means that they are not connected by the same two events.
You fail to explain how if the one going around the gravitational field goes through less curvature than the other light beam. If the one going around travels on a geodesic it obviously goes through a rather curved region of space.

chroot said:

If you care to demonstrate mathematically how such situations are not admissible, I'd love to see you try.

I see, you make the claim and you want me to disprove it.
How about you showing a simple example where you can demonstrate what you say is correct.

Correct, but you claim that the one going around the gravitational field can get there sooner, which by the way means that they are not connected by the same two events.

No, it doesn't.

You fail to explain how if the one going around the gravitational field goes through less curvature than the other light beam. If the one going around travels on a geodesic it obviously goes through a rather curved region of space.

Look at the spacetime diagram shown in the pdf I linked.

How about you showing a simple example where you can demonstrate what you say is correct.

I explained it, gave a reference which explains it very clearly, and provided the common name of the idea -- the Gott loop. What on earth else could I provide you? I didn't make it up -- it's a well-known conclusion.

Yes but your argument was specifically against time travel here remember.

No, my argument was against the assertion that you cannot beat a beam of light, and against that assertion that beating a beam of light means you're travelling through time. Neither assertion is, in fact, true -- at least, not in a unique type of curved spacetimes.